Problem: Which of the following numbers is a multiple of 12? ${77,86,96,109,115}$
Answer: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $77 \div 12 = 6\text{ R }5$ $86 \div 12 = 7\text{ R }2$ $96 \div 12 = 8$ $109 \div 12 = 9\text{ R }1$ $115 \div 12 = 9\text{ R }7$ The only answer choice that leaves no remainder after the division is $96$ $ 8$ $12$ $96$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $96$ $96 = 2\times2\times2\times2\times2\times3 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $96$. We can say that $96$ is divisible by $12$.